Simplify/Condense log base 4 of 192- log base 4 of 3

Problem

(log_4)(192)−(log_4)(3)

Solution

1. Identify the logarithmic property for subtraction, which is the Quotient Rule: (log_b)(M)−(log_b)(N)=(log_b)(M/N)

2. Apply the rule by combining the two logarithms into a single logarithm with the arguments in a fraction.

(log_4)(192/3)

3. Divide the numbers inside the logarithm to simplify the argument.

(log_4)(64)

4. Evaluate the logarithm by determining what power the base 4 must be raised to in order to equal 64

4=64

(log_4)(64)=3

Final Answer

(log_4)(192)−(log_4)(3)=3

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